Title :
Equivalence of Reconstruction From the Absolute Value of the Frame Coefficients to a Sparse Representation Problem
Author :
Balan, Radu ; Casazza, Pete ; Edidin, Dan
Author_Institution :
Siemens Corp. Res. Inc., Princeton, NJ
fDate :
5/1/2007 12:00:00 AM
Abstract :
The purpose of this letter is to prove, for real frames, that signal reconstruction from the absolute value of the frame coefficients is equivalent to solution of a sparse signal optimization problem, namely a minimum lscrp (quasi)norm over a linear constraint. This linear constraint reflects the coefficients relationship within the range of the analysis operator
Keywords :
optimisation; signal reconstruction; signal representation; sparse matrices; absolute value; frame coefficient; linear constraint; reconstruction equivalence; signal optimization problem; signal reconstruction; sparse representation; Constraint optimization; Fast Fourier transforms; Hilbert space; Mathematics; Matrix decomposition; Signal reconstruction; Signal resolution; Sparse matrices; Sufficient conditions; Topology; Frames; nonlinear processing; sparse representation;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2006.888296
